In a semiconductor device including a silicon oxide film as a gate insulation film, in order to prevent so-called boron penetration which is a phenomenon that boron in a gate electrode penetrates the gate insulation film made of the silicon oxide film to reach a substrate, the silicon oxide film is nitrided with plasma and thereafter is subjected to rapid thermal annealing (Patent document 1).    [Patent Document 1] Japanese Patent Application Laid-open No. 2004-48001
However, the above conventional art is an art relating to a MOSFET and requires additional annealing as post-processing. However, the annealing may possibly increase the film thickness. Therefore, there is a demand for an art which can prevent the boron penetration yet does not require the subsequent annealing even in a case where the oxide film forming the gate insulation film of other semiconductor devices, for example, a DRAM (Dynamic Random Access Memory) is processed by plasma nitriding. In this case, it is also necessary to be careful about nitrogen concentration in the oxide film which is a factor to cause deterioration in driving capability of the device.